(* Title: HOL/Arith.thy
ID: $Id$
Author: Lawrence C Paulson, Cambridge University Computer Laboratory
Copyright 1993 University of Cambridge
Arithmetic operators + - and * (for div, mod and dvd, see Divides)
*)
Arith = Nat +
instance
nat :: {plus, minus, times, power}
consts
pred :: nat => nat
(* size of a datatype value; overloaded *)
size :: 'a => nat
defs
pred_def "pred(m) == case m of 0 => 0 | Suc n => n"
primrec "op +" nat
add_0 "0 + n = n"
add_Suc "Suc m + n = Suc(m + n)"
primrec "op -" nat
diff_0 "m - 0 = m"
diff_Suc "m - Suc n = pred(m - n)"
primrec "op *" nat
mult_0 "0 * n = 0"
mult_Suc "Suc m * n = n + (m * n)"
end